# Proving that the matrix is invertible given the eigenvalues?

1. Apr 16, 2012

### theBEAST

1. The problem statement, all variables and given/known data
Given an unknown matrix with eigenvalues 1,2,3, prove that it is invertible?

3. The attempt at a solution
If the det = 0, then there exists an eigenvalue = 0. Since none of the eigenvalues are 0, then the det ≠ 0 and thus the matrix is invertible. Is this a valid proof?

2. Apr 16, 2012

### HallsofIvy

Staff Emeritus
Yes, it is.